How to enter new area?

I cant find any info on how to enter the new area? My friend told me but i forgot and he is asleep, so if anyone would be kind enough telling me that would be great. I only know i need to enter the place in new londo after i kill Ornstein and Executioner Smough. After that im lost, also i have not yet killed the four kings, do i have to kill them to go on or can i skip them for now?

1) talk to Frampt (snake monster in Firelink Shrine) and give him the Lordvessel, upon doing so you'll be treated to a cut-scene which will explain everything

2) go to New Londo and kill the 4 Kings (Sif must be dead and you must be in possession of the Covenant of Artorias Ring) upon doing so another snake monster, this one is name Kaathe, will appear. As you would with Frampt give him the Lordvessel, and, as with Frampt a cut-scene will follow